Bernard is set for an Everton medical on Tuesday.
The attacking midfielder is wanted by a number of top clubs in Europe after running down his contract with Shakhtar Donetsk.
However, Sky Sports believe the Toffees have won the race for his signature.
Bernard has won 14 caps for Brazil and featured at the 2014 World Cup.
West Ham United, Chelsea, AC Milan and Tottenham Hotspur have all tried to sign the 25-year-old.